About Rationally Speaking

Rationally Speaking is a blog maintained by Prof. Massimo Pigliucci, a philosopher at the City University of New York. The blog reflects the Enlightenment figure Marquis de Condorcet's idea of what a public intellectual (yes, we know, that's such a bad word) ought to be: someone who devotes himself to "the tracking down of prejudices in the hiding places where priests, the schools, the government, and all long-established institutions had gathered and protected them." You're welcome. Please notice that the contents of this blog can be reprinted under the standard Creative Commons license.

Monday, April 09, 2012

The Simulation Hypothesis and the problem of natural evil, part I

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by David Kyle Johnson

[This post belongs to a four-part series that Rationally Speaking is running with one of our podcast guests, Prof. David Kyle Johnson of the Department of Philosophy at King’s College in Wilkes-Barre, PA. Kyle's philosophical specializations include logic, metaphysics, epistemology and philosophy of religion. His publications include “God, Fatalism, and Temporal Ontology” (Religious Studies) and “Natural Evil and the Simulation Hypothesis” (Philo). He also teaches and has published extensively on the interaction between philosophy and popular culture, including a textbook (Introducing Philosophy Through Pop Culture) and two edited volumes in the Wiley/Blackwell series (on Christopher Nolan’s Inception and NBC’s Heroes). He maintains the blog Plato on Pop with William Irwin for Psychology Today, and hosts a podcast.]

I have been asked to appear on the live recording of Rationally Speaking at NECSS to talk about the simulation hypothesis and my recently published paper, “Natural Evil and the Simulation Hypothesis” (that will appear in the most recent volume of the journal Philo). In that paper I argue for a fairly controversial thesis: that many theists, given their own philosophical and theological commitments, are logically forced to the conclusion that we live in a computer simulation. In preparation for my appearance I'm going to lay out my argument in four blog entries. First I'll define what philosophers call “the simulation hypothesis” and show why many philosophers think that it’s much more likely than you would suspect. Then I am going to argue that the logical problem of natural evil is commonly misunderstood, and show how it actually presents itself to the modern academic theist. I will then demonstrate the problems with proposed solutions to the problem of natural evil, and why most theists don’t accept them; but we will also see why many such theists claim to not need a solution because they already have reason enough to believe that God exists. Lastly, I will show that embracing this line of reasoning commits them to endorsing the hypothesis that we live in a computer simulation.

So, let’s get started — the simulation hypothesis.

The “simulation hypothesis” suggests that we all, here in the “real” world, actually live in a computer simulation. How could this even possibly be true? How could physical beings, such as us, be in a computer simulation?

It is widely acknowledged that mental activity is a result of brain activity; neuroscience has confirmed this far beyond a reasonable doubt. It is suspected by many that the reason mental activity arises from our brain activity is because of the way our neurons are wired and fire. Consequently, it would seem, anything that replicated the function of our neurons — that is wired and fires like our brains — would have a mind just like ours. But we have also discovered that the function of our neurons can, potentially, be replicated by computer chips. We have already replicated neural firing on a small level — creating artificial retinas, and layers of chips that replicate the activity of our vision centers. Computer chips, it seems, can be wired together, and fire, just like our neurons. This has led some (although this is a bit simplistic) to think of minds as programs being run on the hardware of our brains. If we go with that analogy, we might infer that the program of our minds could potentially be run on something else, like a computer hard drive. And if it was, the same “mind” — the same consciousness — would be realized by that hard drive. Perhaps, if I live long enough, I could copy my mind onto a computer hard drive before my physical body dies, and I could live forever.

More importantly, this has also given rise to the eventual possibility of simulated worlds. Once computing technology has advanced enough, instead of copying an existing person’s mind, and writing it onto a hard drive, one could create a new unique program/mind and copy that onto a hard drive. One could then feed inputs to that program — the same kind of inputs our brains receive from the outside world via our senses. The result? That mind — that simulated person — would experience the same kinds of things we do. He would see objects, feel emotions, hear sounds — in exactly the same way we do. He would thus think that the virtual objects which he sees are physical objects. And you could populate that world with many other beings for that being to interact with, and feed those beings sensations too, thus creating a whole civilization of simulated people living in a simulated environment — that is, a simulated world.

There are many reasons for wanting to do this. Simulated worlds could be of great use to historians. One could see how World War II would’ve turned out had Hitler known about the D-Day invasion. They would be of use to politicians and political scientists. You could examine the consequences of legislation before it is passed. And perhaps most importantly — it would make a really kick-ass Sims game.

The simulation hypothesis suggests that the world we inhabit is a simulated world and that we are simulated persons. And Nick Bostrom has argued this hypothesis is much more likely than you might think. His argument goes like this: If we do create a simulated world, we won’t stop there. We won’t just create one. We didn’t stop with one iPhone; we wouldn’t stop with one simulated world. Once Pandora’s box is open, you can’t close it. If there is one, there will be thousands. And beings in simulated worlds could even advance enough to create their own simulated worlds within their world. So a physical universe with a single simulated world isn’t a very likely scenario. Thus, when we consider the possible physical universes that could exist, we realize the following: either there is one real physical universe and in that universe no simulated world is ever created, or, in the one physical universe that exists, thousands upon millions upon billions of simulated worlds are created.

However, if we one day create a simulated world, then we know that the first kind of universe — the kind of universe with no simulated worlds — is not the kind of universe that exists. The physical universe that exists is one in which billions of simulated worlds are created. The question then becomes, in which do we exist — the one physical universe, or one of the billions of simulated worlds it contains? Well, there is no way to tell from inside a simulated world that one lives in a simulated world. Recall, to its inhabitants, a simulated world looks physical. And since simulated worlds can be created in simulated worlds, the fact that we created a simulated world would not mean ours is not simulated. All we have to go on is the odds. How many physical universes could we inhabit? Only one. How many simulated worlds could we inhabit? Billions! So, given what we know, what are the odds that we don’t live in a simulated world? Billions to one! Infinitesimally small. Creating a simulated world would give us very good reason to believe that we live in a simulated world — indeed, it would be a near guarantee.

So, the epistemic probability of the simulation hypothesis is directly tied to how likely it is that we will, one day, create a simulated world ourselves. If it’s likely that we will create such a world, then it’s likely we live in a simulated world. So, how likely is it that we will, one day, create a simulated world?

Nick Bostrom argues that, given what we know, it’s about 20% likely. There are a number of reasons that we might not create such a world. There may be insurmountable technological boundaries; we might find the ethical objections too convincing; perhaps we will simply lose interest in them; perhaps we will blow ourselves up first. How likely is any one of these scenarios? We really don’t have enough information to tell; humans aren’t good at predicting the future. So, given what we know, we should assign each an equal probability. And since, along with the “we will create a simulated world” hypothesis, there are five possibilities, each one of them gets 20%. So, the likelihood that we will one day create a computer simulated world, given what we know, is 20%. Thus, given what we know, it is 20% likely that we live in a computer simulation.

Now we can quibble with the numbers. Maybe there are more than five options, maybe we should factor in the odds that Hard AI (the notion that computer generated simulated persons can think) is true; so maybe it’s only 10% likely, or 5%. It doesn’t really matter. In any event, it is much more likely than you probably suspected. For certain, the computer simulation hypothesis is more likely than other skeptical scenarios — like the dream hypothesis, or the evil demon hypothesis. And really, that’s all I need for the argument I am about to present.

So, why might a theist be forced to conclude that it is 100% likely that we live in a computer simulation? That has to do with the problem of natural evil, to which I will turn in the next entry.

37 comments:

This - Laplace's principle of indifference - is silly. For one thing, it's trivial to artificially inflate the number of different possibilities by giving them additional qualifiers. Instead of saying, for example, "perhaps we will blow ourselves up first", just say "perhaps we will blow all but 10 people up", "perhaps we will blow all but 11 people up", etc. Presto! You've reduced the probability from 20% to 10% or 5% or ...

The only really honest thing to do, when confronted by so many alternatives for which we really have no way to choose between with current information, is to admit this and move on, not make up phony probability estimates.

Jeff, thanks for your comment. I think Laplace's principle of indifference is far from established as “silly.” Further, I am not artificially inflating the number of possibilities by giving them additional quantifiers. (In fact, doing so would just weaken my case, making the simulation hypothesis less likely; so why would I do that?) All I was doing was considering the 5 possibilities regarding whether or not we will develop a computer simulation—either (1) we will, or (2) limits of technology, (3) ethical considerations, (4) lack of interest, or (5) existential limits (e.g., we destroy ourselves) will keep us from doing so. Those seem to exhaust the possibilities. (Destroying all but 10, all but 11 of us, etc. would fall under the last possibility—although perhaps I stated this possibility too simply in my entry for that to be clear.) And we are dealing with epistemic probability here. If we were dealing with objective probability, yes we probably should just admit that we don’t know what the odds are, and move on. But, when doing epistemic calculations, you assign values “given what you know,” and when you know nothing you assign an equal probability to each option—because, given what you know (nothing), each option is equally likely. And that is what we are dealing with here—epistemic probability. I am just following the rules of epistemic probability here by assigning an each an equal value.

Re: "Destroying all but 10, all but 11 of us, etc. would fall under the last possibility ... "

Nope. It is possible -- though not plausible -- that the remaining n number of humans have both the technical abilities and inclination to simulate a universe. (One of the survivors could be Professor Farnsworth, e.g.)

If probability is defined (crudely) as the long-term proportion with which a certain outcome will occur in situations with short-term uncertainty, the principle of indifference is meaningless: ergo, Jeffrey's comment about the principle's silliness.

Epistemic probabilities are instead understood to be some measure of an agent's degree of belief, explicated in terms, e.g., of fair betting odds. Setting aside other issues, the problem here arises when one (such as yourself) says this:

If we were dealing with objective probability, yes we probably should just admit that we don’t know what the odds are, and move on. But, when doing epistemic calculations, you assign values “given what you know,” and when you know nothing you assign an equal probability to each option—because, given what you know (nothing), each option is equally likely.

If in one context you define probability in terms of frequencies or proportions (cf. "objective probability") and in another define probabilities in terms of measures of degrees of beliefs (or, in this case, ignorance), you must clarify in what way the epistemic probabilities, if they are to be coherent, should map onto the observed relative frequencies in the former case and then in what way we can say the epistemic probabilities in the latter sense are coherent if we have no empirical basis upon which to base the probability assignments in the latter.

In other words, you shift perilously between two incompatible concepts of probability in one sentence. If you want to defend epistemic probabilities, fine: but you cannot defend at the same time a notion of objective probability, for you are then talking about two different concepts.

If Professor Farnsworth was among the survivors—that would fall under the option (1). My point is that the (1)-(5) seem to exhaust the possibilities.

And I’m not jumping back and forth between talking about objective and epistemic probabilities. I am talking about epistemic probabilities—degrees of belief—how confident we should be regarding all this, the entire time. The fact that I mention frequencies or proportions does not mean that I am taking or defining probabilities in objective terms at that point. Objective probabilities can (and should) influence one’s degree of belief, but doing so does not switch one to talking about objective probabilities. For example, my degree of belief that the coin will come up heads is 50%, but that is because I know the objective probability is 50%--but I can still only be making a point about my degree of belief. In addition, ignorance of (or the non-existence of) objective probabilities does not prevent one from assigning epistemic probabilities.

First, the computing power that would be required to convincingly simulate the visible universe would be enormously larger than what appears to be possible *within* our own universe for beings like us (even given quantum computing and science-fiction level resources, like Dyson spheres and supercomputers the mass of Jupiter and so on). This is pretty clear unless P=NP, which is probably not true, and not at all guaranteed to fix these problems even if it was. The laws of physics we encounter appear to become exponentially harder to simulate as you simulate larger and larger systems.

So for the computer simulation hypothesis to work, either whoever is running the simulation must be have at their disposal vastly more computing resources than we can imagine (in which case we cannot readily extrapolate from what we know about our civilization to theirs), or more likely our full universe isn't "really" simulated in full detail (in which case there must be an "evil daemon" that monitors us and simulates phenomena at a finer level only when we are looking too closely at them, to prevent us from finding out that most of the time a much coarser approximation is being used). Perhaps some civilizations only create one or two large-scale simulations because they can never muster the resources for more.

Second, even if we were not a computer simulation, we could be a different sort of simulation. For example, our visible universe (or at least the parts of it that are close enough that they'd be hard to fake) could be made out of "real" physical stuff in "real" physical space, but the entirety of that space might be located inside a giant cosmic petri dish, a possibility that plausibly might require fewer physical resources than simulating the whole thing (much as, at the human level of technology, it may require fewer resources to just test a drug in culture than to accurately simulate how it will act upon living tissue).

Sean, Bostrom argues quite convincingly, in the third section of his original paper, that such computer simulated worlds are well within the possibility of conceivable computing power and the laws of physics. He concludes, “… computing power available to a posthuman [i.e., advanced] civilization is sufficient to run a huge number of ancestor-simulations even it allocates only a minute fraction of its resources to that purpose.” http://www.simulation-argument.com/simulation.html I can’t do justice to his argument in a reply to a comment, but I know of no one who has successfully challenged him on this point. He does consider the possibility of a simulation that only has “fine detail” when needed (like when someone is looking through a microscope), but I don’t think it requires constant attention by a person—the computers could simply be programmed to provide the detail when it detects that we are looking closely.

But I love the petri dish idea—reminds me of a great Simpsons Treehouse of Horror, based on an old Twilight Zone (which, is about half of them) where Lisa creates a civilization in a petri dish that worships her.

"Simulating the entire universe down to the quantum level is obviously infeasible, unless radically new physics is discovered. But in order to get a realistic simulation of human experience, much less is needed – only whatever is required to ensure that the simulated humans, interacting in normal human ways with their simulated environment, don’t notice any irregularities. The microscopic structure of the inside of the Earth can be safely omitted. Distant astronomical objects can have highly compressed representations: verisimilitude need extend to the narrow band of properties that we can observe from our planet or solar system spacecraft. On the surface of Earth, macroscopic objects in inhabited areas may need to be continuously simulated, but microscopic phenomena could likely be filled in ad hoc. What you see through an electron microscope needs to look unsuspicious, but you usually have no way of confirming its coherence with unobserved parts of the microscopic world."

I should say, his attitude towards this fact is much more positive than mine. But I don't think we disagree on any particular fact here. As I was trying to get across, any simulation that can encompass the world we live in must fall somewhere upon the spectrum of "unconceivably vast resources" and "coarse simulation with a evil daemons hiding the coarseness from us". Of course these daemons would not be people, but part of the simulation itself (hence the pun, if you see it), but they must be good enough at understanding and predicting human capabilities and behavior to do their jobs. It's not outlandish to suggest that an entity that can understand and predict human beliefs just by reading brain states may need to be more intelligent in most ways than most actual humans are, in which case we might not even be the smartest or most complex entitities that need to be simulated here!

The simulation must also either simulate, or fill in ad hoc, every part of the environment with a significant chance of significantly influencing human beliefs, whether it actually will so influence us or not, and whether we expect it to influence us or not. (After all, it would not be a very accurate simulation if the natural world never surprised us in highly complex and unlikely ways; that would be a very unlikely universe!)

The main question, then, is how many resources can readily be saved by such daemons without degrading the quality of the simulation to an unacceptable or noticeable level, and without causing the resources used by the daemons themselves to exceed those of the rest of the simulation. Bostrom seems to think that there is a lot of leeway here, and I do not. A convincing simulation of human history has to replicate much of our environment down to a fairly fine level in order to avoid giving up the game, and matching the number of flops executed by the human brain gets you only part of the information necessary to reproduce its workings.

(Simulating a functioning brain, even one very similar to a human brain, is a different problem from producing a population of such brains that are convincingly organic! Besides the physical structures, there are also a significant number of moment-to-moment chemical changes. We get tired or hormonal or drunk. Gene expression changes. Blood pressure fluctuates. Glucose gets used up. Neurotransmitter levels jump up and down. These are effects that are not nice and linear, but often synergistic with each other. None of these can be reasonably expected to affect every neuron, or even every neuron in a very large area, in the same way. At best this adds a few orders of magnitude to the complexity involved, and if you leave most of it out, even if the brain still functions and no one notices, you are no longer simulating something that behaves like a real human brain.)

I'd also like to point out that I think the mass of computers and density of processors are unlikely to be the limiting factors in how large of a computer can be built. Thermodynamic considerations suggest that surface area is of considerable importance. Computers must be powered and cooled, and this must happen through the surface, or else the computer must have an extremely large battery. In either case the energy vented must be greater than that consumed, or else the computer heats up and degrades. Sufficiently large computers also suffer from larger and larger communications costs, though currently that's due to limits in parallelizability that might be surpassed, rather than physical limitations. The same cannot be said for, e.g., Dyson sphere sizes of computers.

All that said, the simulation hypothesis is interesting! But I am suspicious of the suggestion that we know how such computers could be created already, much less that there are good arguments that it is plausible to run several simulations with nesting (there's a significant difference between simulating a universe, and simulating one that can simulate a universe, as Bostrom knows).

I'm also suspicious of the idea that the level immediately "above" ours is significantly likely to resemble our level. Perhaps there are alternative laws of physics that are much more conducive to civilizations harnessing vast amounts of computing power than the laws of physics in our universe. In such a universe it might be trivial to simulate billions of universes like ours just for kicks; some beings might even be able to do it in "organic", evolved brains, the way we do mental arithmetic. What considerations make this more or less likely than a civilization like ours being the one to simulate our universe? The answer is not clear to me, other than that it is easier to imagine something more similar to ourselves.

Yeah, I see what you mean about you and Bostrom being in agreement--you can't simulate a whole universe down to the sub-atmomic level. I guess I am more optimistic about the possibility of a simulated universe, but even if my and Bostrom's optimism is misplaced, I still think I have some reason to think that a computer simulation is possible to some degree--more reason than I have to think that, for example, I am dreaming or being fooled by the evil demon. And, ultimately, that is what I am shooting for here. The simulation hypothesis is the most likely of the scenarios in which our universe is designed, but not designed by God.

Perhaps a better title might be "Why atheists must accept that God runs this simulation". Because whatever runs this simulation has all the characteristics of a deity. One cannot be an atheist and simultaneously believe the Simulation Argument

Dirk, I do think that one could be an atheist and adhere to the simulation hypothesis, at least in the classic sense. God, classically conceived, is all-good, all-knowing, and all-powerful, and a computer programmer need not be any of these things to create a computer simulated world. Even if you equate “God” with “whoever designed our universe”, one who believes our world is a computer simulation need not believe that God exists—for whatever computer programmer designed our world could have died and not shut the simulation down first. If so, Nietzsche was right in a very literal sense—God is dead. But I should probably point out here that I am not arguing that the simulation hypothesis is true. In this entry, I am only arguing that it is more likely than you think. But, ultimately, I am arguing that theists who can’t answer the problem of natural evil are committed to believing the simulation hypothesis. Atheists are not committed to it at all.

BTW, it's not "the" simulation - there are likely to be billions of them. The vast majority would be run by our near term descendants and not be simulating down beyond the neural level. Well within computing capabilities (say) circa 2100CE. As for why - reconstruction of the dead

So lets say this is a simulated world. What does it mean that I'm reading an article about the possibilities of simulated worlds? Is this article simulated by someone also? I think the "creators" are trying to tell me something. Am I a simulation of some one else?

Some of suggested that speculating about the simulation hypothesis is dangerous, because the programer may only find us useful if we don't know that we are in one. Once we figure it out, we'll be shut down. Then again, the programer may be waiting to reward those who figure it out.

Huh, that would suck, but the possibilities it opens about conscience and even ethical concerns is almost to big to wrap one's mind around. The thing about this to me is not whether it is possible but what if it is? So they might have to shut me down.

Jeffrey highlighted one gaping hole of logic in his comment, but there are others. "If we do create a simulated world, we won’t stop there. We won’t just create one." That's a mighty big if. And this huge if is made up of lots of individual large ifs.

In the paragraph beginning "It is widely acknowledged..." Johnson quickly moves on from acknowledged territory. Here are the mushy words from just that paragraph: "suspected by many" "it would seem" "potentially" "it seems" "this is a bit simplistic" "If we go with that analogy, we might infer" "And if it was". How can you take anything that follows that seriously? That's rhetorical, you (and I) can't.

Beyond the specious reasoning, the end of this post is horrid. It is a perfect example of what leads lots of people to declare philosophers are mentally masturbating: "It doesn’t really matter. In any event, it is much more likely than you probably suspected. For certain, the computer simulation hypothesis is more likely than other skeptical scenarios — like the dream hypothesis, or the evil demon hypothesis. And really, that’s all I need for the argument I am about to present."

What? An incredibly improbable scenario is declared more probable than an impossible scenario and that's all that is needed to prove something else? Hogwash.

Mark, I think you are either strawmanning my argument or is just misunderstanding it. The logic of my argument is this: “If A is true, then B is most certainly true. So, to figure out how likely it is that B is true, all we need to do is figure out how likely it is that A is true.” This is not fallacious; it does not contain a gaping logical hole. This is as deductively valid as you can get. If A entails B, then the likelihood of A reflects on the likelihood of B. The mere fact that I use the word “if” does not make it speculative. Mentioning a list of “mushy words” does not either. The point of that “mushily worded” paragraph is simply to argue that Strong AI (a very widely believed philosophical notion that entails that computer simulated persons would be conscious) is likely true, and if it is the possibility of computer simulated worlds follows. If strong AI is not true, then of course they are not possible—but we can just add that to our list of reasons we may never develop simulated worlds: strong AI might be false. And I consider that in the next to last paragraph. All that does is reduce slightly the likelihood of the simulation hypothesis (from 20% to 16%). But since I am not arguing for the truth of the simulation hypothesis—I am only arguing that it is more likely than you probably thought, at least more likely than other skeptical scenarios—this does not endanger my ultimate conclusion. Now, you declare that it is “hogwash” to suppose that this point can be used to make my ultimate point—but you have not even heard how I will use it to make my point. I’m hoping everyone can keep an open mind long enough to at least consider my argument.

Since, in this entry, I was just very quickly summarizing an argument that was published in Philosophical Quarterly (a very prominent philosophical journal), and it is an argument that has been very well received, I didn’t expect so much objection here. But, it might be my fault… I may simply have not been clear enough. So, that said, let me see if I can clear a few things up. Let me post a general comment below, and then I will respond individually to other comments above.

Bostrom has an entire website devoted to this argument—where he has posted his original argument, many different iterations of it, and critical replies, and his responses. For those truly concerned with it, I suggest you check it out. He does a much better job of defending the argument than I ever could. If you can refute his argument, I can guarantee you could get published by doing so.

Re: "If you can refute his argument, I can guarantee you could get published by doing so."

Since when have skeptically-themed arguments been 'refuted'? Contra G.E. Moore, philosophical skepticism, e.g., has never been 'refuted' -- though who among us takes global skepticism seriously?

It is not that one must 'refute' Bostrom's argument. Rather, it is that Bostrom's argument falls, largely, upon our ears as flatus vocis, and for the following reason: It is an unfalsifiable hypothesis in much the same way other skeptical hypotheses are.

You say the simulation hypothesis is more likely to be true than dream-state or evil genius alternatives, but I simply do not see how this is so.

EamonIf Bostrom were arguing that the simulation hypothesis is true, then yeah--you could not "prove" him wrong. Such skeptical conclusions are unfalsifiable by their very nature. But that is not what he is arguing, or what I am arguing.

The last line in his paper (before the conclusion) captures his main thesis best: "Unless we are now living in a simulation, our descendants will almost certainly never run an ancestor-simulation." That is equivalent to: “if our descendants will run an ancestor-simulation then we are almost certainly living in one.” By laying down the (epistemic) odds of whether our descendants will run a simulation, he lays down the (epistemic) odds of whether we are in a simulation. But you could refute his argument by arguing that conditional is false. You also could refute it by arguing, as Sean tried above, that he is off about how likely it is that our descendant will run a simulation (by, for example, casting doubt on their possibility). Arguing against him Iis not about proving that we are not in a computer simulation (an impossibility) since that is not what he is claiming.

But the simulation hypothesis is more likely that the dream or evil demon hypothesis because I have no reason to think the dream or evil demon hypothesis is true. I simply can’t prove them false. But the simulation hypothesis has more going for it than that. It’s not merely unfalsifiable. If our descendants will create one, we are most likely in one—and I at least have some reason to think that our descendants will create one. So I at least have some reason for thinking it's true. That’s the argument.

I won’t rule out the possibility of a simulated world being created in the far away future. But then, I guess, how would I know that the simulated world(s) had not already been started in the far-distant past?

I do not know, if this argument against an infinity of simulated worlds has already been put forward. Suppose that a scientist in the physical world manages to simulate reality. He does this on a hardware with a limited capacity of course. Then the simulated world evolves and a virtual scientist is born. He manages to simulate virtual reality in the first virtual world. For this to be possible the original physical hardware needs to have a capacity of simulating 2 virtual worlds. Of course the scientist in the first virtual world might share his invention with other scientists, or decides to simulate another world, and the same does the scientist in the virtual world inside the first virtual worlds. But all the new virtual world are being simulated on one original physical hardware, which is of limited capacity. This implies that the number of virtual worlds is surely finite, limited with the capacity of the original hardware. This breaks the line arguments of the simulation hypothesis that if there is a simulated world, we almost surely live in one. Not true anymore, since there is a finite number of simulated worlds, therefore the possibility that if there exists a simulated world, we live in one, is equal to 1-1/(n+1), where n stands for a number of simulated worlds. In this case, the (naive) likelihood of us living in a simulated world hinges on the capacity of the original hardware. For the result of infinity of simulated worlds to hold, the physical laws governing the original world need to be different than ours.

Yes, there can't be an infinite number of simulated worlds, but the argument does not rely on there being an infinite number of worlds. Bostrom shows that a post-human civilization could simulate the entire universe using only a faction of a second and only a fraction of their computing power--clearly they could create a simulation capable of housing simulations themselves. That's all the argument need for the argument to work; that means that the fact that we create a simulation is not a reason to think we are not in one.

I completely agree with vasja.it is similar to software emulation.for example, virtualPC, where you can install another guest OS using the host OS. virtualPC emulates all the required hardware components.But at some stage we might decide to install and emulate another sub-guest OS inside the guest OS, we might be able to do so,but this comes at a cost of much slower performance.

computation slows down as the levels of emulation(simulation) go deeper.and there is another problem as vasja mentioned, there can be multiple emulating softwares trying to emulate guest OS' running on the same host OS.

as the guest OS tries to build computational systems(or software enough to emulate another subsystem), we see that there is a lag and this lag affects everything in the hierarchy.

I guess we will never find such a lag(in our universe) when we actually build such simulations.

Sorry, but this statement doesn't follow from any argument you gave in your paper:

"...many theists, given their own philosophical and theological commitments, are logically forced to the conclusion that we live in a computer simulation."

In fact, I believe your paper said as much that it doesn't follow that they are "forced" to such a conclusion. Theists are not "logically forced" to the conclusion that we live in a computer simulation because there are many other possibilities such as that the world is spontaneously created by natural processes (as physicists think) or that we are brain's in vats or we are dreaming, etc. Even if Bostrom is correct that there's a 20% probability we are living in a simulation (and I believe that's a too high) it would entail that your argument suggests we likely *don't* live in a computer simulation. It entails that there's an 80% probability we don't (1.0-.2=.8).

I also don't know about this statement:

"It is widely acknowledged that mental activity is a result of brain activity; neuroscience has confirmed this far beyond a reasonable doubt."

I doubt it. I don't think it is a known fact that this is true. I think there are some philosophies of mind that suggests that consciousness (mental activity) is a product of a whole body computation (central nervous system working together with some other parts of the body) to produce consciousness. I think Antonio Damassio defended such a thesis too. I remember also reading a paper that argued that it's not only the brain but the immediate, external, physical environment that produces consciousness. The brain and the sensory system has to interact with the immediate environment in just the right ways to produce consciousness. Conscious mental activity "supervenes" on that whole system.

I don't know, you might be right that the brain alone can do that stuff but it seems overstated to say that it's "far beyond a reasonable doubt" that mental activity is a result of brain activity. It's also overstated that theists are "forced" to the conclusion that we live in a computer simulation. It's more like they are "forced" (assuming Bostrom is right which is in itself a huge assumption) that we only have a 20% probability that we live in such a world.

Yeah, the world "logically" is probably too strong there--I should have said "rationally forced." Since, given their commitments, they are logically forced to conclude that someone else created our universe, and the simulation hypothesis is the most likely such scenario, the most rational thing to conclude is that we are in a simulation--but there are other logically possible scenarios where God is not the creator of our universe that they could chose if they are willing to be irrational by rejecting the most likely scenario.

I didn't say we are certain that mental activity is the result of brain activity, but I think it is clearly beyond a reasonable doubt and thus I would say that we know it. No neuroscienist I know of would take whole body computation seriously. For sure, our brains interpret signals from our body to produce mental phenomena--but, as we have already seen, such signals can be produced artificially. You can take parts of the body away, and the mind will still function. This is not true of the brain--you take parts of the brain away, and the mental goes away with it. (Although, I guess, you could replace that part of the brain with something else and the mental activity would still likely arise--but it seems that the brain function, that interprets what the body sends to it, plays a more direct role in producing consciousness than the body that is sending the signals.)

But even if you are right, this doesn't effect the argument--it just means that it is in virtue of the computer simulating our brain and whatever-else (central nervous system) that simulated persons are minded. The conclusion still goes through.